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Do a Timeline Distribution Before doing a Weibull Failure Analysis
Weibull Analysis has become popular as a means of identifying equipment parts’ failure patterns.
The shape of the failure curve allows us to identify whether the failure mode was an ‘early life’
failure, a randomly induced failure or due to wear-out and aging. The Weibull shape parameters
provides the owners, users and maintainers of equipment with a tool to use the failure history of
their operating plant and predict the behaviour of components and items of equipment replaced
complete. The analysis directs selection of effective equipment maintenance strategies and design-
out efforts to reduce parts failure.
Figure 1 – Six Failure Patterns for Parts (only applies to ‘parts’, not overhauled assemblies)
Waloddi Weibull identified the Weibull distribution in 1937 while seeking a formula for the failure
rate of welds. It is now one of the most commonly used methods for fitting equipment life data and
used extensively in the aviation industry to optimise maintenance intervention and select
maintenance strategy. The essence of Weibull’s work was to discover he could represent the
Bathtub Curve of Figure 2 using mathematical formula. His equation could mimic the behaviour of
a combination of other statistical distributions, which were each of limited use, by changing its
shape. It could represent all the zones of the bathtub curve by using the three Weibull parameters -
beta β (shape parameter), eta η (life) and gamma γ (start location).
Figure 2 - Weibull Wear-out Life Curve
β < 1 implies infant mortality. Electronic and mechanical components often have high failure rates
initially. Some components are purposely ‘burnt in’ prior to use, while others require careful
BATHTUB CURVE
β < 1 (steep fall) β = 1 (flat) β > 1 (steep rise)
Infant Mortality Zone Design Life Wear out Zone
B
A
C
D
E
F
Age of Equipment
Age Related Patterns Random Incident Patterns
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commissioning after installation. The presence of infant mortality indicates poor training, lack of
procedures and poor quality control.
β = 1 implies random failures. These failures are independent of time where an old part is as good
as a new part. Maintenance overhauls are not appropriate for random failures. Condition
monitoring and inspection are strategies used to detect the onset of failure, and reduce the
consequences of failure. This zone is affected by random incidents and accidents. It reflects poor
operating procedures, poor risk management and poor materials selection at design.
1< β <4 implies early wear out. You would not expect this type of failure within the design life.
Failure mechanisms such as corrosion, erosion, low cycle fatigue and bearing failures fall in this
range. Maintenance often involves a periodic rework or life extension task. The shape can be
altered by better materials selection, by degradation management and by good control of operating
practices.
β > 4 are wear-out or end of life failures. They should not appear in the design life. Age related
failures include stress corrosion cracking, creep, high cycle fatigue, and erosion. Appropriate
maintenance is often renewal of the item with new.
An ideal profile for equipment is to have a negligible failure probability throughout its operating
life followed by a steep beta that predicts the replacement age. Figure 3 shows such a profile.
Figure 3 - Ideal Failure Profile for Parts
A drawback of Weibull analysis is the implied assumption that the future is the same as the past.
As soon as design, maintenance or operating policies and practices change, the prior failure history
becomes unrepresentative of the future. An analysis using the old data would produce poor
decisions in that case. Weibull Analysis requires complete and accurate failure data over a period
of stable practices, along with an analyst who has thorough understanding of the effects of past and
current maintenance and operating policies and practices.
Weibull Analysis is used on failures of the same mode. This is most important, a Weibull plot only
applies to one failure mode of an item. It is a false analysis to predict the life of a part that fails for
several reasons (e.g. a bearing can have several failure modes - overload, distortion, run short of
lubricant, run with water in the lubricant, etc), or for a complex machine made of many parts. You
must plot each part’s failure modes separately1. Note that in Weibull Analysis a ‘part’ is defined as
1 Sherwin, David., Retired Maintenance and Reliability Professor, ‘Introduction to the Uses and Methods of Reliability Engineering with particular
reference to Enterprise Asset Management and Maintenance’ Presentation, 2007.
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a replaceable item. Provided the complete assembly or equipment is replaced at every failure,
Weibull Analysis can be used for complex systems. For example, if a mechanical seal, or a drive
coupling, or gearbox fails and each is always replaced with a complete assembly, then the
mechanical seal, coupling and gearbox are seen as a ‘part’. If however the assembly is stripped, the
failed parts replaced, and the repaired assembly reinstalled, then it is not suitable for Weibull
Analysis. A part replaced in the assembly would qualify for analysis, but not the entire rebuilt
assembly.
Beware that repeated overhauls of complex equipment result in ever decreasing times between
failures after each overhaul. When old parts are reused from one overhaul to the next, the
equipment has increasing chance that it will fail sooner than last time. The reused parts are already
fatigued and distorted. When used again they fail sooner because prior service stresses reduce their
remaining usable life. Having already had a life, they are perhaps close to the end. It is good
strategy to identify when equipment parts have accumulated too many service hours of use, or too
many overstress cycles, and replace the entire equipment with new2.
Weibull Analysis predicts probabilistic safe intervals for operation. It helps in selecting the
optimum maintenance type and interval so the cost of spares and downtime are minimised for
maximum reliability. With sufficient failure data points Weibull Analysis can advise if Preventive
and Predictive Maintenance, or re-design, be investigated to improve a component’s reliability.
With Weibull Analysis, you can compare the cost and estimated effectiveness of your options. You
can determine if re-design, or extra quality precautions in manufacture, or whether to initiate
measures to reduce operational loads and stresses, are the best choice for the business. It applies to
deciding warranty periods, shutdown intervals and setting maintenance and inspection intervals.
Accurate Weibull Analysis needs trustworthy parts failure data with clear failure modes. With a
sophisticated CMMS in use, the collection of failure mode data is more reliable and data analysis
can be done electronically.
Many organisations have kept records of failures manually or in computer systems, but not used the
data in any useful way. Failure data is the best source of reliability information available. It is
relevant and site people can relate their own experience to it. By transforming maintenance and
parts history into useful data used to make failure forecasts, it models the benefits of alternative
strategies, or analyses the reliability of current systems and their capacity to meet operating needs.
Life Cycle Simulation
Once the Weibull parameters that best fit failure mode behaviours are available, they can be used to
simulate performance over extended periods. If you have a mathematical model of a part’s past,
you can use the same model to predict its future. Provided the part is treated the same in future as it
was in the past, the model is believable. Modern simulation packages involve a Monte Carlo
simulation engine that generates random effects in accordance with the historic Weibull parameters
over a specified system lifetime. It attempts to mimic what will happen to the part in service if its
future were to remain the same as its past. Used in conjunction with FMECA principles, the
process of selecting maintenance and inspection intervals becomes a process of playing ‘what if’
with the Weibull software by comparing the probabilistic effects of different reliability strategies.
You then know how to adjust your maintenance to bring the most benefits to the business.
2 Gurgenci, Hal., Zhihqiang, Guan, ‘Mobile Plant Maintenance and the Duty Meter Concept’, Journal of Quality in Maintenance Engineering, Vol 7,
No4, 2001
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Example Weibull Analysis
It is first necessary to separate each failure into its specific failure mode. Ideally about 10 data
points are required for each failure mode to ensure a robust analysis. Too few points for a failure
mode causes uncertainty that the Weibull equations are the best fit for the data and so any
interpretation from the curves cannot be trusted.
In Figure 4 the mining truck fleet tyre failures collected during service are colour coded by failure
mode. The assessment of each failure is by experienced and knowledgeable technicians proficient
in tyre failure analysis. Each mining truck tyre costs about $150,000 and the sum of the failures and
replacements is about $28 million.
Figure 4 Truck Tyre Failure Events by Failure Mode
The first activity in a Weibull Analysis is not to do a Weibull Analysis, just yet. First plot the
failure mode events in a timeline to make sure the data makes sense. Age related failures should
have a timeline clearly related to age or usage. Random failure events should have a timeline
evidencing ad-hoc occurrences. Early life failures should show-up soon after parts started into
operation.
Figure 5 shows distribution charts of the various tyre failure modes. The failure data was manually
put into a spreadsheet from the colour coded table which was then used to create the distribution
plots. Even without drawing Weibull failure curves the timeline distributions tell a clear story.
Tyre wear is mostly grouped between 30,000 to 40,000 kilometres. It is clear that increased
stocking of tyres will be necessary as trucks in the fleet near 30,000 km. Punctures, side wall
damage and rock damage are operational procedure problems. It would be a smart, proactive
decision to more regularly grade the roads on which these mining trucks operate. The 43 tyres lost
to un-kept roads cost $6.5 million, an amount which would more than adequately cover the cost of
the extra road grading to protect the tyres against damage.
Much can be learnt from failure mode time distributions even without using Weibull curve plotting
software.
Piling the Dead - Tyre Replacement/ FailureChanged normal wear Changed side-wall damage Changed tire defective Changed alignment accelerated wear
Failued due to wear Failed side-wall damage Failed due to other reasons
Failed from puncture Changed rock damage Changed unbalance accelerated wear
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Figure 5 Failure Mode Event Timeline Distributions
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A close look at the distances of unbalance and poor alignment failures show them starting at about
10,000km with each mode causing frequent loss of tyres thereafter. An immediate maintenance
strategy that becomes evident is to schedule all trucks for tyre balance and alignment every
10,000km. The more than 40 tyres lost from these two preventable failure modes is worth over $6
million. With all trucks coming in for a service every 10,000km anyway the additional balance and
alignment would add an extra day off the road and cost a technician’s time. A full costing model
needs to be developed to be sure savings will be gained, but on face value it seems that the inclusion
of alignment and balance preventive maintenance will make money for the operation.
Example Weibull Plots on Weibull Graph Paper
The computer screen dumps below show the Weibull failure curves for various tyre failure modes,
along with the calculation tables developed for the Weibull curve equations. The data points are
plotted on Weibull graph paper, which was developed for Weibull failure analysis before computer
software was commercially available. When you learn Weibull Analysis you are first required to
plot failure data using Weibull graph paper and you only use computer programs later once you are
accomplished with manual graphing.
The closeness with which the individual data points match the straight line through them all is an
indication of the suitability of using a Weibull curve to fit the data. The nearer to being on a
straight line where the data points plot on the graph paper the more sure you are that Weibull math
is the appropriate distribution to use.
From each failure mode graph the three Weibull parameters - beta β (shape parameter), eta η
(characteristic life) and gamma γ (start location) can be identified.
Figure 6 is for tyres’ normal wear failure mode. It has a beta of 7, which means a strongly age
related failure. The gamma indicates no wear-out failures are likely until 22,000km. The tyres’
characteristic life (by which 62.7% of tyres have failed) due to wear-out is 42,000km.
Figure 7 shows the Weibull plot for all tyres lost to rock damage of various modes. The expectation
is that all such damage would be random since no one can know when a rock will damage or
puncture a tyre. Up until about 30,000km the beta is 1, which identifies random failure. But after
30,000km the curve has a strong age related bias. One possible reason for the hip is that once tyres
have built-up stresses from 30,000km of service they are more prone to rock damage due to their
accumulated inner fatigue.
The Weibull plot of Figure 8 is only for tyres changed due to rock damage. The beta of 2.4
confirms wear and tear is a factor affecting when tyres start suffering damage from rocks. Here
again one is suspicious that tyre fatigue weakens tyres and makes them more susceptible to damage
from rocks.
By using a timeline and doing Weibull Analysis of each failure mode your maintenance history can
provide you with a very sound understanding of that is happening to your plant and equipment and
what you can do to improve reliability and reduce operational and maintenance costs.
My best regards to you,
Mike Sondalini
www.lifetime-reliability.com
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Figure 6 Tyre Wear-Out Failure Mode
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Figure 7 All Rocks Damage Failure Mode
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Figure 8 Just Tyres Changed from Rocks Damage Failure Mode
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